Reynolds equations for common generalized Newtonian models and an approximate Reynolds-Carreau equation

Exact, closed-form, one-dimensional Reynolds equations are presented for the Ostwald-DeWaele model, the Ellis model, the Spriggs model, and the double-Newtonian Rabinowitsch and Ferry models. From numerical solutions for flowrate, an approximate Reynolds- Carreau equation is obtained. These models describe the wide range of constitutive shear responses that have been observed in lubricants at elevated pressure. It is hoped that the equations presented here will enable researchers to perform full elastohydrodynamic lubrication (EHL) simulations of the coupled elasticity and Reynolds equations for shear-thinning liquids.